Sample size planning for the noninferiority or equivalence of a linear contrast with cost considerations

Tests of equivalence have been used by psychological and social researchers to demonstrate the equivalence of 2 group means. However, there is a need for better methods of sample size planning if there are more than 2 groups and the aim is to carry out a linear contrast of population means, especially if cost constraints and variance heterogeneity among groups are considered. Therefore, this study presents an iterative procedure of sample size estimation for testing the linear contrast of noninferiority/ superiority and equivalence, respectively, by using the proposed group size allocation ratios, especially if some group sizes are fixed at certain values. The proposed method has the advantages of minimizing total cost at the designated power or maximizing the statistical power if the total budget has a limit. Three illustrative examples show the key points of the proposed approach the effectiveness of determining sample sizes is demonstrated in terms of empirical Type I errors and power of computer simulation. Because software or applets to determine the sample size for equivalence and noninferiority/superiority testing are not widely available, the authors provide R programs for ease of use. They conclude by emphasizing the need for systematic thinking on sample size planning with regard to the related research and evaluation frameworks, and some directions for further research are also discussed.